MATH1012 - Lecture 18

← Back to Home

MATH1012 - Lecture 17
Slides Wk6

Finding Limits

• For a recursive sequence, we can find what limit it converges to
  • Assuming the sequence has a limit
• We replace all sequence terms in the iteration by the limit $a$
  • Then solve for $a$

---

Slides Wk7

Partial Sums

• $s_n=a_1+a_2+...+a_n$
  • i.e. a series is the sum of the values in a sequence
• $a_n=s_n-s_{n-1}$
• If the sequence of partial sums converges to $L$ as $n\to \infty$, then we say: ${\sum }_{n=1}^{\infty }{a}_n=L$
  • If $\underset{n\to \infty }{\lim }{a}_n\ne 0$ then ${\sum }_{n=1}^{\infty }{a}_n$ does not exist (does not converge)

---

MATH1012 - Lecture 19
Annotated Slides